Instability of zonal flows in a two‐layer shallow water semi‐geostrophic model

The parametric dependence of the instability of zonally symmetric basic flows is examined in a two‐layer shallow water semi‐geostrophic (TLSWSG) model on the f ‐plane. The relevant parameters are the Rossby number ( Ro ), domain aspect ratio (µ), and Burger number ( B ). The cut‐off values of the Burger and Richardson numbers ( Ri ) for stability are estimated for a constant shear basic flow based on the pseudo‐energy and pseudo‐momentum conservation equations. Unstable normal‐mode growth rates are calculated for a wide range of parameters for a constant shear basic flow and a cosine‐type basic flow. The results show that within the SG regime, a small Burger number tends to generate strong baroclinic instability for a constant shear basic flow, but tends to suppress barotropic–baroclinic instability for a cosine‐type basic flow. Increasing the Rossby number enhances both baroclinic and barotropic–baroclinic instability when B >0.16 but reduces the instability of large‐scale disturbances when B <0.16. Strong anisotropy (large µ) leads to strong barotropic–baroclinic instability for a cosine‐type basic flow, but tends to reduce baroclinic instability for a constant shear basic flow. It is also found that strong horizontal shear tends to suppress baroclinic instability. Copyright © 2005 Royal Meteorological Society